A beer barrel flatpack can be made at a workbench (Wooden workbench or better) in the workshop of a player-owned house. This requires 7 Construction and 1 Cooking, uses 3 planks, 3 nails, and gives 87 experience. The flatpack can then be used on the barrel space hotspot in the Kitchen while in building mode. This requires no Construction level and gives no experience.
The cost of making and selling a beer barrel flatpack from scratch gives a profit of -2,159. This assumes the nails did not break, and steel nails (highest nail available at sawmill) were used.
After completing the hard Fremennik Tasks, they can also be traded to Advisor Ghrim in exchange for 59 coins being added to your kingdom's coffers in Miscellania. See Flatpack: Miscellania reselling for details.